Recently, the sterile neutrino \(N\)  as a portal to the dark sector via the Yukawa coupling \(\lambda _{ds} \bar{\chi }\phi N\)  is receiving increasing interest [1]}, [2]}, [3]}, [4]}, [5]}. In this paper, we consider the fermion singlet \(\chi \)  as dark matter. For a sizable coupling \(\lambda _{ds}\) , the secluded channel \(\bar{\chi }\chi \rightarrow NN\)  is important to obtain correct relic density, which is also observable at indirect detection experiments [6]}, [7]}, [8]}. The DM-nucleon scattering cross section is one-loop suppressed, thus is easy to escape the tight direct detection limits. On the other hand, correct relic density can also be obtained for tiny via the freeze-in mechanism [9]}, [10]}, [11]}, [12]}, [13]}. Although the DM \(\chi \)  is hard to detect at canonical direct and indirect detection experiments, the delayed decay of dark scalar \(\phi \)  into light neutrinos will affect the Big Bang Nucleosynthesis (BBN) predictions, the Cosmic Microwave Background (CMB) anisotropy power spectra, the effective number of relativistic neutrino species \(N_{\rm eff}\)  and the energetic neutrino spectra observed today [14]}, [15]}, [16]}, [17]}.
